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arXiv · 2410.20453

The best $m$-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$

Kateryna Pozharska·Anatolii Romanyuk
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Abstract

Exact order estimates are obtained of the best $m$-term trigonometric approximations of the Nikol'skii-Besov classes $B^r_{p, \theta}$ of periodic functions of one and many variables in the space $B_{q,1}$. In the univariate case ($d=1$), we get the orders of the respective approximation characteristics on the classes $B^r_{p, \theta}$ as well as on the Sobolev classes $W^r_{p, {\boldsymbol{\alpha}}}$ in the space $B_{\infty,1}$ in the case $1\leq p \leq \infty$.

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Kateryna Pozharska, Anatolii Romanyuk. 2024-10-27. The best $m$-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$. https://arxiv.org/abs/2410.20453

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